Three-Dimensional Orthogonal Graph Drawing with Optimal Volume

An orthogonal drawing of a graph is an embedding of the graph in the rectangular grid, with vertices represented by axis-aligned boxes, and edges represented by paths in the grid that only possibly intersect at common endpoints. In this paper we study three-dimensional orthogonal drawings and provide lower bounds for three scenarios: (1) drawings where the vertices have a bounded aspect ratio, (2) drawings where the surfaces of vertices are proportional to their degrees, and (3) drawings without any such restrictions. Then we show that these lower bounds are asymptotically optimal, by providing constructions that in all scenarios match the lower bounds within a constant factor.     

On Embedding a Graph in the Grid with the Maximum Number of Bends and Other Bad Features

Graph Drawing is (usually) concerned with the production of readable representations of graphs. In this paper, instead of investigating how to produce “good” drawings we tackle the opposite problem of producing “bad” drawings. In particular, we study how to construct orthogonal drawings with many bends along the edges and with large area. Our results show surprising contact points, in Graph Drawing, between the computational cost of niceness and the one of ugliness.     

Orthogonal drawings and crossing numbers of the Kronecker product of two cycles

An orthogonal drawing of a graph is an embedding of the graph in the plane such that each edge is representable as a chain of alternately horizontal and vertical line segments. This style of drawing finds applications in areas such as optoelectronic systems, information visualization and VLSI circuits. We present orthogonal drawings of the Kronecker product of two cycles around vertex partitions of the graph into grids. In the process, we derive upper bounds on the crossing number of the graph. The resulting upper bounds are within a constant multiple of the lower bounds. Unlike the Cartesian product that is amenable to an inductive treatment, the Kronecker product entails a case-to-case analysis since the results depend heavily on the parameters corresponding to the lengths of the two cycles.     

Diagonal stability of a class of cyclic systems and its connection with the secant criterion

We consider a class of systems with a cyclic interconnection structure that arises, among other examples, in dynamic models for certain biochemical reactions. We first show that a “secant” criterion for local stability, derived earlier in the literature, is in fact a necessary and sufficient condition for diagonal stability of the corresponding class of matrices. We then revisit a recent generalization of this criterion to output strictly passive systems, and recover the same stability condition using our diagonal stability result as a tool for constructing a Lyapunov function. Using this procedure for Lyapunov construction we exhibit classes of cyclic systems with sector nonlinearities and characterize their global stability properties.     

Layout modeling and construction procedure for the arrangement of exhibition spaces in a fair

This paper tackles a subset of layout problems that is not a subject of the scientific research to date: the arrangement of the exhibition spaces in a fair. A fair is a large‐scale exhibition for goods and services; for example a trade fair or a regional fair. The layout problem of fairs consists in finding an acceptable layout for both the exhibitors, the visitors, and the organizer of the fair. A model for representing the layout of fairs is presented: the adjacency model. Based on the adjacency model, a construction procedure is developed that leads to the generation of alternative layout solutions. Numerical results for the layout of a real fair are reported.     

Simulations of the dynamic behavior of a bipedal robot with trunk and arms subjected to 3D external disturbances in a vertical posture, during walking and during object handling

This paper provides a new approach to the bipedal robot stability problems in presence of external disturbances in vertical posture of the robot, during walking and during object handling. This approach is based on synergy between the dynamic motions of balancing masses and arms to reject large perturbations applied to the upper part of ROBIAN robot. In these cases, the stabilization is carried out in the first time with a trunk having 4 degrees of freedom (dof): one rotational and three translational movements. In the second time, the stabilization is performed with a system with arms and having 10 dof. During the walk, the trunk elements of ROBIAN reproduce necessary movements to perform the dynamic walking gait of the robot. The compensation of external three-dimensional efforts applied to the robot is achieved firstly by the trunk and secondly with the arms. This study allows us to determine on-line the required movements and accelerations of the trunk elements in order to maintain the robot stability and shows the importance of the arms for the robot stability.